President Barack Obama and House Speaker John Boehner left Washington without a deal.

By David Lightman

McClatchy Newspapers

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WASHINGTON -- When President Barack Obama and Congress return to Washington later this week, the countdown to the fiscal cliff will be measured in days -- yet no one really knows how, when or even whether an agreement might be reached.

Sorting out the scenarios is like trying to assemble a 100-piece puzzle on deadline. About the only decent bet is the one offered by Sen. Joe Lieberman, a Connecticut Independent:

"We're going to spend New Year's Eve here, I believe," he told CNN on Sunday.

There are four general ways the drama is likely to unfold:

• No deal at all.

• The long-elusive big deal.

• Consideration of legislation that one chamber already passed.

• A small time-buying accord that would require further negotiations.

If no alternative is adopted, Bush-era income tax cuts will expire Dec. 31. On Jan. 2, $109 billion in automatic spending cuts would take effect, and half of them would involve defense.

Those are just the big items, however.

Extended unemployment benefits for an estimated 2.1 million Americans begin expiring at the end of this month. Also ending would be the 2-percentage-point Social Security payroll-tax cut and the alternative minimum tax patch. The AMT, originally aimed at wealthy taxpayers who avoided high taxes with deductions, wasn't indexed to inflation, and therefore it could affect 31 million people unless Congress approves a change.

It's difficult to gauge sentiment for agreements. Though Obama pleaded with congressional leaders Friday to work something out, Republicans in the House of Representatives remained defiant.

Even as the president used his weekly Saturday radio address to offer a holiday greeting, House Speaker John Boehner used much of the Republicans' own weekly address to talk politics.

But if the negotiating chaos of recent years has taught anything, it's not to pay too much attention to the public sniping. Obama, Boehner, Senate Majority Leader Harry Reid, D-Nev., Senate Republican leader Mitch McConnell, R-Ky., and their staffs are expected to talk privately.

Here are the likely scenarios:

No deal. Few on Capitol Hill will say it publicly, but there's a lot of talk about how each side can benefit politically if the stalemate continues past Jan. 1. And if the markets don't react once the cliff is reached, there might be even less incentive to get a quick deal.

There also might be a new incentive to act. Because higher tax rates would go into effect, getting a tax deal might become easier. Lawmakers could argue that they're now cutting taxes for lower- and middle-income people while keeping them intact for wealthy people.

Big deal. Obama and Boehner weren't that far apart when they traded offers last week, and for all the sniping, there are messages of hope in their remarks.

Pending legislation. There are vehicles available to lawmakers that would enable them to move quickly. The House passed a measure in August to continue all the Bush income-tax rates for a year. The Senate adopted a measure in July to maintain those rates for all but individuals who earn more than $200,000 a year and families that make more than $250,000, the same limits Obama backed.

Small deal. There are more fiscal crises on the horizon: A new debt-limit ceiling is likely to be needed in mid-February and current fiscal-year spending runs out March 27.

Congress and the president might extend the tax rates or avoid some spending cuts and couple that with one of the other upcoming crises in the hope that a big deal could be worked out later. Such a smaller deal also would be easier to get through Congress before Jan. 1.